November 2009 Paper 4

2) (a) Use your calculator to work out the value of 8.7 x 12.3 9.5 – 5.73 Write down all the digits from your calculator. Give your answer as a decimal. 107.01 = 28.384615… 3.77 (b) Write your answer to part (a) correct to 1 significant figure. 30 (to 1 sf)

3) (a) p = 2 q = – 4 Work out the value of 3p + 5q 3x2 + 5x-4 (1 mark) = 6 + -20 = -14 (1 mark) (b) Factorise 3m – 6 3 (m – 2)

4). Frank did a survey on the areas of pictures in a magazine 4) Frank did a survey on the areas of pictures in a magazine. The magazine had 60 pages. Frank worked out the area of each of the pictures in the first 2 pages. This may not be a good method to do the survey. Explain why. Comment to say either sample size is too small or the first two pages may not be representative of the whole magazine

5) (a) On the diagram, draw in one plane of symmetry for the prism. (b) In the space below, sketch the front elevation from the direction marked with an arrow.

6)i)Write down the size of the angle marked a. 45° (ii) Give a reason for your answer. Corresponding angles are equal

7) A circle has a radius of 5 cm. Work out the area of the circle. Give your answer correct to 3 significant figures. Area = πr2 Area = π x 52 Area = 78.53981634 Area = 78.5cm2 (3sf)

8) Soap powder is sold in two sizes of box. Small box Large box Which size of box gives the better value for money? Explain your answer. You must show all your working. Soap Powder 9kg £7.65 Soap Powder 2kg £1.72

8) Soap powder is sold in two sizes of box. A small box contains 2 kg of soap powder and costs £1.72. A large box contains 9 kg of soap powder and costs £7.65. Which size of box gives the better value for money? Explain your answer. You must show all your working. £1.72 ÷ 2 = £0.86 per kg for small box £7.65 ÷ 9 = £0.85 per kg for large box Therefore large box is better value for money.

9). Describe fully the single transformation 9) Describe fully the single transformation that maps triangle A onto triangle B Rotation (1 mark) 180° (1 mark) Centre (0,1) (1 mark) Generally: Rotation is worth 3 marks Reflection is worth 2 marks You get no marks if you write down more than one transformation e.g. rotate then translate

10) A computer costs £360 plus 17½ % VAT. Calculate the total cost of the computer. 10% = 36 5% = 18 2.5% = 9 17.5% = 63 Total cost = 360 + 63 = £423

11) (a) What type of correlation does this scatter graph show? Negative The time a car takes to go from 0 mph to 60 mph is 11 seconds. (b) Estimate the maximum speed for this car. Draw a line of best fit and read your answer off this line to guarantee the mark. Answer = 118 to 123

12) The lengths of the sides of the triangle are 2x + 9, 2x – 3, 4x + 5 Find an expression, in terms of x, for the perimeter of the triangle. Give your expression in its simplest form. 2x + 9 + 2x – 3 + 4x + 5 = 8x + 11 The perimeter of the triangle is 39 cm. (b) Find the value of x. 8x + 11 = 39 8x = 28 x = 28/8 = 3.5

13) A piece of wood is 180 cm long. Tom cuts it into three pieces in the ratio 2 : 3 : 4 . Work out the length of the longest piece. 2 + 3 + 4 = 9 180 ÷ 9 = 20 20 x 4 = 80

14) The equation x3 + 2x = 60 has a solution between 3 and 4 Use a trial and improvement method to find this solution. Give your answer correct to 1 decimal place. You must show all your working. Answer = 3.7 (1 mark) x x3 + 2x 3.5 49.875 too low (1 mark) 3.7 58.053 3.8 62.472 too high 3.75 60.234375

15) (a) Simplify m3 × m4 m7 (add the powers) (b) Simplify p7 ÷ p3 p4 (subtract the powers) (c) Simplify 4x2y3 × 3xy2 12x3y5 (deal with numbers and each letter separately)

16) ABC is a right-angled triangle. AB = 14 cm. BC = 12 cm. Calculate the length of AC. Give your answer correct to 3 significant figures. Right angled triangle – trigonometry or Pythag AC is longer side AC2 = 142 + 122 AC2 = 196 + 144 = 340 AC = 340 = 18.4cm (3sf)

a) Complete the table of values for y = x2 – 3x – 1 Work out positive values of x first If you are given a negative value of x with a corresponding y value check you can get the answer Use the graph to check your y values look right x -2 -1 1 2 3 4 y -9 -3

b) Plot points from your table and make sure they look right Graphs should not have ‘corners’ Points should be joined with either a straight line or a smooth curve (1,-3) and (2,-3) should not be joined with a straight line

18) The table shows some information about the heights (h cm) of 100 students. (a) Find the class interval in which the median lies. 150<h<160 Height (h cm) Frequency 120<h<130 8 130<h<140 16 140<h<150 25 150<h<160 30 160<h<170 21

18) The table shows some information about the heights (h cm) of 100 students. (b) Work out an estimate for the mean height of the students. 14900 ÷ 100 = 149 Height (h cm) Frequency Midpt 120<h<130 8 125 1000 130<h<140 16 135 2160 140<h<150 25 145 3625 150<h<160 30 155 4650 160<h<170 21 165 3465 100 14900

19)a) Expand and simplify (x – 3)(x + 5) x2 + 5x – 3x – 15 = x2 + 2x – 15 (b) Solve 29 – x = x + 5 4 29 – x = 4x + 20 29 = 5x + 20 9 = 5x x = 9/5

(b) Use the moving averages to describe the trend. Increasing 124 63 20) (a) Work out the four-point moving averages for this information. The first three have been worked out for you. £83 £86 £88 £90 (b) Use the moving averages to describe the trend. Increasing Month Jan-Mar 2007 Apr-Jun 2007 Jul-Sep 2007 Oct-Dec 2007 Jan-Mar 2008 Apr-Jun 2008 Jul-Sep 2008 Cost of Gas 124 63 24 121 136 71 32 124 + 63 + 24 + 121 4 63 + 24 + 121 +136 4 24 + 121 + 136 + 71 4 121 + 136 + 71 + 32 4

21) In a sale, normal prices are reduced by 12%. The sale price of a digital camera is £132.88 Work out the normal price of the digital camera. £132.88 = 88% £1.51 = 1% £151.00 = 100%

24)The table below gives some information about some students in a school. Andrew is going to carry out a survey of these students. He uses a sample of 50 students, stratified by year group and gender. Work out the number of Year 13 girls that should be in his sample. 85/382 x 50 = 11.12... Ans = 11 Year Group Boys Girls Total Year 12 126 94 220 Year 13 77 85 162 203 179 382

25) y is directly proportional to x. When x = 500, y = 10 (a) Find a formula for y in terms of x. y = kx 10 = k(500) k = 10/500 = 1/50 y = 1/50x (b) Calculate the value of y when x = 350 y = 1/50 (350) y = 7

28) v = a b a = 6.43 correct to 2 decimal places. b = 5.514 correct to 3 decimal places. By considering bounds, work out the value of v to a suitable degree of accuracy. You must show all your working and give a reason for your final answer.

28) v = a b a = 6.43 correct to 2 decimal places. b = 5.514 correct to 3 decimal places. Upper bound = 6.435 = 1.08034 5.5135 Lower bound = 6.425 = 1.07840 5.5145 v = 1.08 (2dp)

Solve 4 + 3 = 1 x + 3 2x – 1 4(2x – 1) + 3 (x + 3) = 1(2x – 1)(x + 3) 8x – 4 + 3x + 9 = 2x2 + 6x – x – 3 11x + 5 = 2x2 + 5x – 3 0 = 2x2 – 6x – 8 0 = x2 – 3x – 4 0 = (x – 4)(x + 1) x = 4 or x = -1